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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25  \chapter*{Notations} \begin{figure}[h] \begin{center} \begin{tabular}{|l|l|} \hline $n$ & number of variables\\ $\bx=(x_1,x_2,\ldots,x_n)^T \in\RR^n$ & the unknown\\ $\bx_0\in\RR^n$ & the initial guess\\ $\bv\in\RR^n$ & a vertex\\ $S=\{\bv_i\}_{i=1,m}$ & a complex, where $m\geq n+1$ is the number of vertices\\ $S=\{\bv_i\}_{i=1,n+1}$ & a simplex (with $n+1$ vertices)\\ $(\bv_i)_j$ & the $j$-th component of the $i$-th vertex\\ $S_0$& the initial simplex\\ $S_k$& the simplex at iteration $k$\\ $\bv_i^{(k)}$& the vertex $i$ at iteration $k$\\ $f^k_i = f\left( \bv_i^(k) \right)$& the function value of the vertex $i$ at iteration $k$\\ $f:\RR^n\rightarrow\RR$& the cost function\\ \hline \end{tabular} \end{center} \caption{Notations used in this document} \label{fig-notations} \end{figure}